System and Method for Returning a House Advantage in a Game of Chance

ABSTRACT

A form of play is disclosed that provides a house advantage in a blackjack side game.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.13/911,918, filed Jun. 6, 2013, which is a continuation-in-part of U.S.patent application Ser. No. 13/340,423, filed Dec. 29, 2011, whichapplication claims priority to U.S. provisional patent application Ser.No. 61/429,520, filed Jan. 4, 2011, each of which is incorporated hereinin its entirety by this reference thereto.

BACKGROUND OF THE INVENTION

1. Technical Field

The invention relates to games of chance. More particularly, theinvention relates to a system and method for returning a house advantagein a game of chance.

2. Description of the Background Art

Blackjack, also known as Twenty-one or Vingt-et-un (French:“twenty-one”), is the most widely played casino banking game in theworld. Blackjack is a comparing card game between a player and dealerand played with one or more French decks of 52 cards.

The player is dealt an initial two card hand with the option of drawingcards to bring the total value to 21 or less without exceeding it, sothat the dealer will lose by having a lesser hand than the player or byexceeding 21. Many rule variations of blackjack exist. Since the 1960s,blackjack has been a high profile target of advantage players,particularly card counters, who track the profile of cards yet to bedealt, and adapt their wager and playing strategy accordingly.

At a casino blackjack table (see FIG. 1), the dealer faces between fiveto seven playing positions 10 from behind a semicircular table. At thebeginning of each round, up to three players place their bets in a“betting box” 12 at each position in play. The player whose bet is atthe front of the betting box is deemed to have control over theposition, and the dealer will consult the controlling player for playingdecisions regarding the hand; the other players of that box are said to“play behind.” Any player is usually allowed to control or bet in asmany boxes as desired at a single table, but it is prohibited to play onmore than one table at a time or to place multiple bets in a single box.

Each box is dealt an initial hand of two cards visible to the peopleplaying on it, and often to any other players. The dealer's handreceives its first card face up, and in “hole card” games receives itssecond card face down immediately (the hole card), which the dealerpeeks at but does not reveal unless it makes the dealer's hand ablackjack. Hole card games are sometimes played on tables with a smallmirror or electronic sensor which are used to peek securely at the holecard. In European casinos, “no hole card” games are prevalent; thedealer's second card is neither drawn nor consulted until the playershave all played their hands.

Cards are dealt either from one or two hand-held decks, from a dealer'sshoe, or from a shuffling machine. Single cards are dealt to each ofwagered-on position clockwise from the dealer's leftmost position,followed by a single card to the dealer, followed by an additional cardto each of the positions in play. The players' initial cards may bedealt face-up, or face-down (more common in single-deck games).

The players' object is to win money by creating card totals which willturn out to be higher than the dealer's hand, but without exceeding 21(“busting”/“breaking”). On their turn, players must choose whether to“hit” (take a card), “stand” (end their turn), “double” (double wager,take a single card and finish), “split” (if the two cards have the samevalue, separate them to make two hands) or “surrender” (give up ahalf-bet and retire from the game). Number-cards count as their naturalvalue; the jack, queen, and king (also known as “face cards” or“pictures”) count as 10; aces are valued as either 1 or 11 according tothe player's best interest. If the hand value exceeds 21 points, itbusts, and all bets on it are immediately forfeit. After all boxes havefinished playing, the dealer's hand is resolved by drawing cards untilthe hand busts or achieves a value of 17 or higher (a dealer total of 17including an ace, or “soft 17,” must be drawn to in some games and muststand in others). The dealer never doubles, splits nor surrenders. Ifthe dealer busts, all remaining player hands win. If the dealer does notbust, each remaining bet wins if its hand is higher than the dealer's,and loses if it is lower. In the case of a tied score, known as “push”or “standoff”, bets are normally returned without adjustment; however, ablackjack beats any hand which is not a blackjack, even with value 21.Blackjack vs. blackjack is a push. Wins are paid out at 1:1, or equal tothe wager, except for winning blackjacks, which are traditionally paidat 3:2, or one and a half times the wager. Many casinos today payblackjacks at less than 3:2 at some tables.

Blackjack games almost always provide a side bet called insurance, whichmay be played when dealer's upcard 14 is an ace. At least one furtherside bet is usually provided.

If the dealer's upcard is an ace, the player is offered the option oftaking “insurance” before the dealer checks the hole card.

Insurance is a side bet that the dealer has blackjack and is treatedindependently of the main wager. It pays 2:1 and is available when thedealer's exposed card is an ace. The idea is that the dealer's secondcard has a fairly high probability (nearly one-third) to be ten-valued,giving the dealer blackjack and disappointment for the player. It isattractive (although not necessarily wise) for the player to insureagainst the possibility of a dealer blackjack by making a maximum“insurance” bet, in which case the “insurance proceeds” will make up forthe concomitant loss on the original bet. The player may add up to halfthe value of their original bet to the insurance and these extra chipsare placed on a portion of the table usually marked “Insurance Pays 2 to1.”

Players with a blackjack may also take insurance, and in taking maximuminsurance they commit themselves to winning an amount exactly equal totheir main wager, regardless of the dealer's outcome. Fully insuring ablackjack against blackjack is thus referred to as “taking even money,”and paid out immediately, before the dealer's hand is resolved; theplayers need not produce to place more chips for the insurance wager.

Insurance bets are expected to lose money in the long run, because thedealer is likely to have blackjack less than one-third of the time.However the insurance outcome is strongly anti-correlated with that ofthe main wager, and if the player's priority is to reduce variation, itis reasonable to pay for this.

Furthermore, the insurance bet is susceptible to advantage play. It isadvantageous to make an insurance bet whenever the hole card has morethan a chance of one in three of being a ten. Advantage play techniquescan sometimes identify such situations. In a multi-hand, face-up, singledeck game, it is possible to establish whether insurance is a good betsimply by observing the other cards on the table after the deal; even ifthere are just 2 player hands exposed, and neither of their two initialcards is a ten, then 16 in 47 of the remaining cards are tens, which islarger than 1 in 3, so insurance is a good bet. This is an elementaryexample of the family of advantage play techniques known as cardcounting.

Bets to insure against blackjack are slightly less likely to beadvantageous than insurance bets in general, since the ten in theplayer's blackjack makes it less likely that the dealer has blackjacktoo.

Many blackjack tables offer a side bet on various outcomes including:

-   -   Player hand and dealer's up card sum to 19, 20, or 21 (“Lucky        Lucky”);    -   Player initial hand is a pair (“Perfect pairs”);    -   Player initial hand is suited, suited and connected, or a suited        K-Q (“Royal match”);    -   Player initial hand plus dealer's card makes a flush, straight,        or three-of-a-kind poker hand (“21+3”);    -   Player initial hand totals 20 (“Lucky Ladies”);    -   Dealer upcard is in between the value of the players two cards        (“In Bet”);    -   First card drawn to the dealer will result in a dealer bust        (“Bust It!”);    -   One or both of the players cards is the same as the dealers card        (“Match the Dealer”); and    -   Player allowed to make optional second hand, and effectively        receive the hand of 10, 8, or 18 without drawings cards        (“Instant 18”).

The side wager is typically placed in a designated area 16 next to thebox for the main wager. A player wishing to wager on a side bet isusually required to place a wager on blackjack. Some games require thatthe blackjack wager should equal or exceed any side bet wager. Anon-controlling player of a blackjack hand is usually permitted to placea side bet regardless of whether the controlling player does so.

The house edge for side games is generally higher than for the blackjackgame itself. Nonetheless side games can be susceptible to card counting,often requiring bespoke counting systems. Most side games do not offersufficient win rate to justify the effort of advantage play; exceptionsare “Lucky ladies” and “Over/Under”.

It would be advantageous to provide a house advantage in a blackjackside game.

SUMMARY OF THE INVENTION

The invention comprises a form of play that provides a house advantagein a blackjack side game.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic view of a blackjack game board;

FIG. 2 shows a Dealer Bust 21 pay table according to the invention;

FIG. 3 is a table that shows the Dealer Bust 21 house advantage,depending on the pay table used, the number of decks, and the houserules, according to the invention; and

FIG. 4 is a block schematic diagram that depicts a machine in theexemplary form of a computer system within which a set of instructionsfor causing the machine to perform any of the herein disclosedmethodologies may be executed.

DETAILED DESCRIPTION OF THE INVENTION

The invention comprises a form of play that provides a house advantagein a blackjack side game. An embodiment of the invention is referred toa Dealer Bust 21.

Rules for Dealer Bust 21

1. Dealer Bust 21 is a blackjack side bet, available for blackjack dealtfrom 1, 2, 6, or 8 decks.

2. The player must place a blackjack bet to play the Dealer Bust 21 sidebet.

3. If a player chooses to participate, an additional Dealer Bust 21wager is placed in the designated area on the layout 16 (see FIG. 1).

4. In an embodiment, all bets must be placed prior to the dealer dealingany cards. In other embodiments, bets may be placed after the dealerbegins dealing cards.

5. The Dealer Bust 21 side bet is resolved based on the final result ofthe dealer's hand.

6. If one or more players make a Dealer Bust 21 side bet, then thedealer must play out his hand according to the house rules, regardlessof whether all players have busted, have blackjack, or there otherwiseare no players remaining with live blackjack hands.

7. The player wins the Dealer Bust 21 side bet if the dealer busts. Theplayer is paid by reference to an associated one or one or more paytables for the game and dealer upcard 14 (see FIG. 1). FIG. 2 shows aDealer Bust 21 pay table.

8. Otherwise, if the dealer does not bust, the player loses and forfeitshis Dealer Bust 21 wager.

Pay Tables and House Advantage

The four pay tables shown in FIG. 2 are available for the Dealer Bust 21side bet. Other embodiments of the invention may have more or fewer paytables. The pay table for a particular game is selected by the player orthe house, based upon house rules, size of bet, etc. The payouts aredivided into four categories based on the dealer upcard:

-   -   The bust cards, 2, 3, 4, 5, 6;    -   The intermediate cards, 7, 8, 9;    -   The face cards, T, J, Q, K; and    -   An ace, A.

For example, in the pay table 3, all pays are the same (2-to-1) for adealer bust. In pay table 4, the player is paid 4-to-1 if the dealerbusts with a non-bust card, otherwise the player is paid 1-to-1 (evenmoney) for a dealer bust.

FIG. 3 is a table that shows the Dealer Bust 21 house advantage,depending on the pay table used, the number of decks, and the houserules. The rule that the dealer must hit soft 17 is denoted H17. Therule that the dealer must stand on soft 17 is denoted S17. Note that thedealer busts more often with the H17 rule than with the S17 rule.Therefore, for a fixed pay table, the game is more player-favorable withthe H17 rule than the S17 rule.

Methodology for the Mathematical Analysis of the Dealer Bust 21Blackjack Side Bet

The Dealer Bust 21 blackjack side bet was analyzed using programswritten in the C++ programming language and combinatorial analysis. Alldealer hands were played out in every possible way for every combinationof dealer-up card (A, 2, 3, 4, 5, 6, 7, 8, 9, T, J, Q, K), number ofdecks (1, 2, 6, 8) and house rules (I-117, SI7). The results weretabulated and imported into Excel to complete the combinatorialanalysis. Every house advantage given in FIG. 3 was audited using acomputer program written in C++ that performed a Monte Carlo simulation.Each simulation consisted of at least one hundred million (100,000,000)rounds. The dealer bust frequencies were compared to results obtainedfrom www.wizardofodds.com. These audits were consistent with thecomputations and combinatorial analysis given herein.

Computer Implementation

FIG. 4 is a block schematic diagram that depicts a machine in theexemplary form of a computer system 1600 within which a set ofinstructions for causing the machine to perform any of the hereindisclosed methodologies may be executed. In alternative embodiments, themachine may comprise or include a network router, a network switch, anetwork bridge, personal digital assistant (PDA), a cellular telephone,a Web appliance or any machine capable of executing or transmitting asequence of instructions that specify actions to be taken.

The computer system 1600 includes a processor 1602, a main memory 1604and a static memory 1606, which communicate with each other via a bus1608. The computer system 1600 may further include a display unit 1610,for example, a liquid crystal display (LCD) or a cathode ray tube (CRT).The computer system 1600 also includes an alphanumeric input device1612, for example, a keyboard; a cursor control device 1614, forexample, a mouse; a disk drive unit 1616, a signal generation device1618, for example, a speaker, and a network interface device 1628.

The disk drive unit 1616 includes a machine-readable medium 1624 onwhich is stored a set of executable instructions, i.e., software, 1626embodying any one, or all, of the methodologies described herein below.The software 1626 is also shown to reside, completely or at leastpartially, within the main memory 1604 and/or within the processor 1602.The software 1626 may further be transmitted or received over a network1630 by means of a network interface device 1628.

In contrast to the system 1600 discussed above, a different embodimentuses logic circuitry instead of computer-executed instructions toimplement processing entities. Depending upon the particularrequirements of the application in the areas of speed, expense, toolingcosts, and the like, this logic may be implemented by constructing anapplication-specific integrated circuit (ASIC) having thousands of tinyintegrated transistors. Such an ASIC may be implemented with CMOS(complementary metal oxide semiconductor), TTL (transistor-transistorlogic), VLSI (very large systems integration), or another suitableconstruction. Other alternatives include a digital signal processingchip (DSP), discrete circuitry (such as resistors, capacitors, diodes,inductors, and transistors), field programmable gate array (FPGA),programmable logic array (PLA), programmable logic device (PLD), and thelike.

It is to be understood that embodiments may be used as or to supportsoftware programs or software modules executed upon some form ofprocessing core (such as the CPU of a computer) or otherwise implementedor realized upon or within a machine or computer readable medium. Amachine-readable medium includes any mechanism for storing ortransmitting information in a form readable by a machine, e.g., acomputer. For example, a machine readable medium includes read-onlymemory (ROM); random access memory (RAM); magnetic disk storage media;optical storage media; flash memory devices; electrical, optical,acoustical or other form of propagated signals, for example, carrierwaves, infrared signals, digital signals, etc.; or any other type ofmedia suitable for storing or transmitting information.

Although the invention is described herein with reference to thepreferred embodiment, one skilled in the art will readily appreciatethat other applications may be substituted for those set forth hereinwithout departing from the spirit and scope of the present invention.Accordingly, the invention should only be limited by the Claims includedbelow.

1. A method for returning a house advantage in a game of chance,comprising: providing a game of chance having both a blackjack bet and aside bet; requiring a player to place a blackjack bet as a condition forplacing a side bet; if a player chooses to place a side bet, receivingfrom the player an additional wager in a designated area on a playlayout; resolving said side bet based on a final result of the dealer'shand; wherein if one or more players make a side bet, then the dealermust play out his hand according to house rules, regardless of whetherall players have busted, have blackjack, or there otherwise are noplayers remaining with live blackjack hands; wherein the player wins theside bet if the dealer busts; wherein the player is paid by reference toa pay table for the game and a dealer upcard; wherein if the dealer doesnot bust, the player's wager is lost and forfeited; wherein payouts aredivided into four categories based on a dealer upcard as follows: bustcards, 2, 3, 4, 5, 6; intermediate cards, 7, 8, 9; face cards, T, J, Q,K; and ace, A; and wherein said pay tables comprise any of: Outcome ofPay Dealer's Dealer Table Pay Table Pay Table Pay Table Hand Upcard #1#2 #3 #4 Dealer A 10  15  2 4 Busts Dealer T, J, Q, K 4 4 2 4 BustsDealer 7, 8, 9 2 2 2 4 Busts Dealer 2, 3, 4, 5, 6 1 1 2 1 Busts DealerAny lose lose lose lose Doesn't Bust


2. The method of claim 1, wherein said side bet comprises a blackjackside bet for blackjack dealt from any of 1, 2, 6, or 8 decks.
 3. Themethod of claim 1, wherein all bets must be placed prior to a dealerdealing any cards.
 4. A method for returning a house advantage in a gameof chance, comprising: a game of chance having both a blackjack bet anda side bet; said game requiring a player to place a blackjack bet as acondition for placing a side bet; if a player chooses to place a sidebet, the player placing an additional wager in a designated area on aplay layout; resolving said side bet based on a final result of thedealer's hand; wherein if one or more players make a side bet, then thedealer must play out his hand according to house rules, regardless ofwhether all players have busted, have blackjack, or there otherwise areno players remaining with live blackjack hands; wherein the player winsthe side bet if the dealer busts; wherein the player is paid byreference to a pay table for the game and a dealer upcard; wherein ifthe dealer does not bust, the player's wager is lost and forfeited;wherein payouts are divided into four categories based on a dealerupcard as follows: bust cards, 2, 3, 4, 5, 6; intermediate cards, 7, 8,9; face cards, T, J, Q, K; and ace, A; and wherein said pay tablescomprise any of: Outcome of Pay Dealer's Dealer Table Pay Table PayTable Pay Table Hand Upcard #1 #2 #3 #4 Dealer A 10  15  2 4 BustsDealer T, J, Q, K 4 4 2 4 Busts Dealer 7, 8, 9 2 2 2 4 Busts Dealer 2,3, 4, 5, 6 1 1 2 1 Busts Dealer Any lose lose lose lose Doesn't Bust


5. The methods of claim 4, wherein said side bet comprises a blackjackside bet for blackjack dealt from any of 1, 2, 6, or 8 decks.
 6. Themethod of claim 4, wherein all bets must be placed prior to a dealerdealing any cards.